Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

Journal of Industrial Engineering International

دوره 11، شماره 4، اسفند 2015   

نویسندگان

Majid Khedmati؛ Seyed Taghi Akhavan Niaki^*

Department of Industrial Engineering, Sharif University of Technology, Azadi Ave., P.O. Box 11155-9414, 1458889694, Tehran, Iran

چکیده

Assuming a first-order auto-regressive model for the auto-correlation structure between observations, in this paper, a transformation method is first employed to eliminate the effect of auto-correlation. Then, a maximum likelihood estimator (MLE) of a step change in the parameters of the transformed model is derived and three separate EWMA control charts are used to monitor the parameters of the profile. The performance of the proposed change-point estimator is next compared to the one of the built-in change-point estimator of EWMA control chart through some simulation experiments. The results show that the proposed MLE of the change point accurately estimates the true change point and outperforms the built-in estimator of EWMA chart for almost all shift values and auto-correlation coefficients, while the built-in estimator of EWMA chart, in general, underestimates the true change point.

کلیدواژه‌ها

Change point . Maximum likelihood estimator (MLE) . Step change . Simple linear profile . Within؛ profile auto؛ correlation